In a mixing bowl, combine the lime juice, olive oil, minced garlic, cumin, chili powder, salt, black pepper, and paprika to create the marinade.
Add the chicken breasts to the marinade, ensuring they are well-coated. Cover and refrigerate for at least 30 minutes (or up to 2 hours for more flavor).
Preheat the grill or grill pan over medium-high heat.
Remove the chicken from the marinade and discard any leftover marinade. Grill the chicken for 5-7 minutes on each side or until the internal temperature reaches 165°F (75°C) and the chicken is cooked through.
While the chicken is grilling, prepare the avocado salsa. In a separate bowl, combine the diced avocados, cherry tomatoes, red onion, cilantro, lime juice, salt, and pepper. Gently mix to combine.
Once the chicken is fully cooked, remove it from the grill and let it rest for a few minutes.
Slice the chicken and serve it topped with the fresh avocado salsa.